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Differentiating Math Instruction
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Differentiating Math Instruction
Strategies That Work for K-8 Classrooms

Second Edition
Edited by:


152 pages | Corwin
'Bender presents a variety of ways to differentiate instruction and foster dynamic learning' — Scott Currier, Mathematics Teacher, Belmont High School, NH

'This is one of those rare opportunities when a teacher can read a book and become inspired to take ideas immediately back to the classroom' — Amanda P. McKee, Math Instructor, Florence £5 School District, Johnsonville, SC

Differentiate math instruction with practices that boost mastery for all students!

Experienced teachers understand and appreciate that all students learn and process information according to their individual styles, abilities, and preferences. William N. Bender provides teachers with a wealth of critical strategies and teaching ideas for differentiating instruction to leverage each learner's unique abilities and raise student achievement in math.

With updated information and recommendations based on the 2008 National Mathematics Advisory Panel report, this new edition of Differentiating Math Instruction includes research on the value of brain-compatible teaching and creative ways to get students visualizing, vocalizing, and moving during math to make instruction more meaningful, motivational, and successful. New and seasoned teachers alike will be able to quickly adapt the techniques to suit their specific classrooms, with key features including:

- Strategies for use within a Response to Intervention framework

- At-a-glance lists of "Top Ten Tactics" for successful implementation

- "Web Site Reviews" that outline additional online resources

- Concrete strategies to tap into multiple intelligences

- A facilitator's guide for staff developers to train teachers in differentiating math instruction

Engage every student in a deep conceptual understanding of mathematics with this key resource aimed at revitalizing mathematics instruction in the elementary and middle school classroom.

 
Preface: How to Use This Book
 
Acknowledgments
 
About the Author
 
1. The Mathematical Brain and High-Impact Teaching
Teaching Mathematics Through Differentiating Instruction

 
The Mathematical Brain

 
Brains as Prioritizing Filters

 
Number Sense

 
Multiple Intelligences: Avenues for Learning Math

 
Summary of Brain Research

 
Instructional Phases for Developing Math Skills

 
Teaching Strategy: Mathematical Games to Develop Number Sense

 
SHEMR: A Tool for High-Impact Learning in Mathematics Evaluating One’s Own Instructional Planning

 
What’s Next?

 
 
2. Differentiated Instruction and Response to Intervention in Mathematics
Differentiation and Response to Intervention: Refocusing Math Instruction

 
Teaching Phases in the Direct Instruction Lesson

 
Problems With Direct Instruction in a Large Class

 
Teaching Strategy: The Guess, Assess, and Tear Out Tactic

 
A Differentiated Instruction Lesson Example

 
Teaching Strategy: Using Guess, Assess, and Tear Out! Moving From Direct Instruction to Differentiated Instruction in Math

 
The Omega Group

 
The Mainline Instruction Group

 
The Beta Group

 
Is Further Differentiation Needed?

 
Anything Wrong With This Scenario? Enhancing the Differentiated Instruction Model

 
Guidelines for Differentiated Lesson Planning

 
Results of Differentiated Lessons

 
A Differentiated Instruction Overview: What It Is and What It Isn’t

 
Response to Intervention in Mathematics

 
Case Study: A RTI for Number Sense and Early Math Skill

 
What’s Next?

 
 
3. Differentiating for Primary and Elementary Math
Research on Math Readiness

 
Steps in Developing Early Math Skills

 
Teaching Strategy: A Concrete, Semi-Concrete, Abstract Learning Tactic

 
Using CSA in the Classroom

 
CSA in the Higher Grades

 
Summary: CSA Tactic

 
Teaching Strategy: The Errorless Learning Procedures

 
Summary: Errorless Learning

 
Teaching Strategy: Classwide Peer Tutoring for Differentiating in the Math Class

 
What’s Next?

 
 
4. Differentiating for Deep Conceptual Understanding
High-Impact Teaching for Operations in Math

 
The Debate on Calculators in Elementary Mathematics

 
Constructivist Theory and Understanding of Mathematics

 
Using Cognitive Guided Visualization

 
Scaffolded Instruction in Math

 
Debate on What a Scaffold Is

 
Graphic Representations of Word Problem Schemas

 
Using a Representational Strategy

 
Teaching Expanded Notation and Partialing

 
Process Mnemonics Strategies to Teach Computation

 
Research Support

 
What’s Next?

 
 
5. Differentiating With Learning Strategies
The Brain Research Basis for Metacognitive Theory and Tactics

 
Learning Strategies for Word Problems

 
The Schema-Based Math Strategy

 
Differentiated Tear Out Activities for Story Problem Schemas

 
What’s Next?

 
 
6. Differentiating in the Middle Grades
Working Toward Higher-Order Thinking

 
Teaching Strategy: Anchored Instruction

 
Teaching Games in Higher Grades

 
The PASS Strategy

 
Moving On Up! Math Instruction Guidelines for Secondary Learners

 
 
Appendix
 
References
 
Index

"This is one of those rare opportunities when a teacher can read a book and become inspired to take ideas immediately back to the classroom and use them. This book provides an effective plan to help teachers reach all their students using proven and researched strategies. It guides today's classroom teacher who is struggling to help a diverse student population become successful."

Amanda P. McKee, Math Instructor
Florence #5 School District, Johnsonville, SC

"This book provides refreshing strategies that work in the classroom. Bender has presented us with a variety of ways to differentiate instruction and foster dynamic learning. This work is a gift to individuals who are constantly looking for ways to improve their practice."

Scott Currier, Mathematics Teacher
Belmont High School, NH

"William Bender's book should be a necessity for the bookshelf of anyone who teaches math. It speaks to the educator who may be struggling to reach all math learners in his or her classroom. It also reaches the math coach who is inspired by Bender's work and who wishes to spread this wealth of knowledge to other educators. There is truly something for everybody."

Carl Ameen Jr., Principal
Allendale Elementary School, Pittsfield, MA

"A fantastic resource for first-year teachers and veterans alike. Bender’s research base combines with creativity and multiple approaches to yield a great reference that teachers can use over and over again."

Randy Wormald, Mathematics Teacher, Belmont High School, NH
Former Math Teacher, Londonderry Junior High School

"The structure of the book invites teachers to enter into the text based on their questions—by design, a differentiated resource! The book is an excellent choice for a study group to begin the conversation on differentiation in mathematics. The inclusion of a facilitator's guide provides further questions and activities for deepening teachers' understanding of differentiation in mathematics."

Thelma A. Davis, Principal
Clark County School District, Las Vegas, NV
Key features
New and seasoned educators alike will be quick to put the following key features to use in their classrooms:

  • "Ideas From Teachers" sections that highlight actual examples of the differentiation process in action
  • At-a-glance lists of "Top Ten Tactics" for successful implementation in K-8 classrooms
  • "Web Site Reviews" that outline additional online resources for effective mathematics instruction
  • Concrete strategies to tap multiple intelligences
Research on the value of brain-compatible teaching is combined with teacher-generated tips, including creative ways to get students visualizing, vocalizing, and moving during math-to make instruction more meaningful, motivational, and successful.

While the new edition remains structurally similar to the previous edition, the author made many revisions throughout the text. He added new references to recent research on learning and mathematics, including statistics on mathematics achievement and new studies about the brain. In addition, the author updated the material by explaining how differentiated math instruction correlates with the recommendations made by the National Mathematics Advisory Panel in 2006. The book includes a list of selected recommendations from the panel's report. Several new teaching strategies and examples have been included, as well as sections about response to intervention. In these sections the author includes explanations of RTI, case studies of RTI in mathematics, and figures to illustrate the intervention process.

Preview this book

Sample Materials & Chapters

Preface

Chapter 1: The Mathematical Brain and High Impact Teaching


William N. Bender

Learn more about William Bender's PD offeringsConsulting Description: Differentiated InstructionConsulting Description: MathConsulting Description: Project-Based LearningConsulting Description: RTIConsulting Description: Technology  William N. Bender began his career by teaching eighth- and ninth-grade students in the public schools. He worked in higher education for 28 years and published over 60 research articles and 24 books in education. He specializes in instructional strategies for all students and is recognized as a national leader on instructional tactics, response to intervention, and differentiated instruction. Dr.... More About Author

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